Hi all,

I guess this is more of a programming question, but I am hoping to find some
deeper theoretical results:

The "ode45" of Matlab and other functions solve ODE numerically on a range
of points, such as in the following example:

Example
[t,y]=ode45(@vdp1,[0 20],[2 0]);
plot(t,y(:,1));
solves the system y' = vdp1(t,y), using the default relative error
tolerance 1e-3 and the default absolute tolerance of 1e-6 for each
component, and plots the first component of the solution.

Here [0, 20] is a range of the "t" variable...

Now what if I want the solution on a set of discrete data points.

Programmatically, I can of course call the above ODE multiple times, or
compute a range first and then sift out some point values...

But those are not efficient, is there an efficient way inside Matlab and/or
outside Matlab can allow me to solve ODEs on a set of data points more
efficiently?

Thanks!